In the electronics industry, the size of devices, including integrated circuits (IC) and micro electro-mechanical systems (MEMS), continues to shrink to reduce footprint and power consumption. For technologies having a critical dimension smaller than 45 nanometers (nm), as integrated circuit critical dimension is reduced and its circuit density increases, the minimum separation distance between adjacent lines approaches the resolution limit of the 193 nm optical exposure tools used in optical lithography. Due to high capital costs, it is desirable to continue using previously purchased lithography tools. Thus, compensation techniques, such as optical proximity correction (OPC) have been developed. OPC alters the photomask design to compensate for distortions caused by diffraction and produce circuit patterns in the substrate which more closely conform to the IC designer's layout.
Computational Lithography techniques are being developed to calculate appropriate photomask shapes to for producing desired features on a wafer. For example inverse lithography technology (ILT) mathematically derives optimal mask shapes for a particular light source and circuit pattern shape. Sub-resolution model based assist features (hereinafter, “assist features”) can be added to the photomask, to improve the accuracy of the circuit pattern on the wafer. Because of the diffraction effects, these assist features are not patterned on the semiconductor wafer itself. Source mask optimization (SMO) optimizes the light source of critical design parts and appropriate OPC for that light source is performed. These techniques result in a mask design having curvilinear mask patterns.
To prepare the curvilinear mask patterns for forming the photomask using an e-beam writer, the patterns are “fractured” into sequences of rectangles or triangles. For example, to form a horizontal or vertical line, a sequence of abutting rectangles is formed. To form a diagonal line, a sequence of overlapping rectangles is provided. This process is referred to as “Manhattanization.” The rectangles may then be further fractured into smaller abutting rectangles. The Manhattanization/fracturing process involves a long computer execution time.